Selected publications by R.M. Brannon

For an ungrouped up-to-date list, refer to the publications section of BrannonCV.pdf

Tutorials and "how-to" guides

• Student Tutorials on Topics in Mechanics: A collection of "how to" documents for students. Topics include Mohr's circle, Tensor analysis, Kinematics of deformation, continuum mechanics, etc.

Computational Constitutive modeling

Computational Plasticity and Generalized Plasticity

• Elements of Phenomenological Plasticity: Geometrical Insight, Computational Algorithms, and Topics in Shock Physics, a book chapter on the equations governing plasticity theory, how those equations are solved numerically, and how they perform in shock physics applications.
• THE SANDIA GEOMODEL: Theory and User's Guide: A comprehensive (detailed) description of a three-invariant differentiable cap plasticity model suitable for applications to rock mechanics and flexible enough to simplify to other plasticity models typically used for metals and viscous media. This user's guide provides tutorial information about stress invariants and tensor analysis, methods for visualizing stress paths, nonlinear plastically coupled elasticity, kinematic and isotropic hardening, rate dependence (viscoplasticity via a Duvaut-Lions overstress model), verification, validation, calibration, and sample input sets.
• On a viscoplastic model for rocks with mechanism-dependent characteristic times: summarizes the theory of the Sandia GeoModel and provides experimental evidence that rate dependence depends on the mechanism of inelasticity. In particular, pore collapse appears to be more "sluggish" than shear cracking failure.
• Unified Compaction/Dilation, Strain-Rate Sensitive, Constitutive Model for Rock Mechanics Structural Analysis Applications: A formal publication describing the Sandia GeoModel.

Statistical Uncertainty in Material Properties

• The Influence of Uncertainty in Crack or Slip Plane Orientations on Cracking or Localization Probabilities, presented at the American Society of Civil Engineers (ASCE) 9th Specialty Conference on Probabilistic Mechanics and Structural Reliability, Albuquerque, NM, 2004. This paper describes how uncertainty in crack sizes and orientations leads to a Weibull-like scale-dependent statistical distribution of failure strength. Note: The American Society of Civil Engineers (ASCE) appears to have never received conference proceedings from the conference organizers. Consequently, a full citation for this paper is unavailable. It will have to be treated as a web document.

Continuum Mechanics

• Caveats concerning conjugate stress and strain measures and related viewgraphs entitled The distinction between large distortion and large deformation: This document contains an analytical solution for the stress in a fiber reinforced composite in the limit as the matrix material goes to zero stiffness. Because the solution is exact for arbitrarily large deformations, it can be used to illustrate subtle concepts in large deformation continuum mechanics.

Computer Visualization

• Visualization of Geological Stress Perturbations Using Mohr Diagrams: Using an ancient tensor visualization tool (Mohr's circle) in a modern computing context.
  
  
• Exploring 2D Tensor Fields Using Stress Nets: Using an ancient tensor visualization tool (Mohr's circle) in a modern computing context.

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